Absorption and Dispersion of Ultrasonic Waves

ContentsPreface List of Notations Introduction A. General Theory of Relaxation in Fluids I. The Stokes-Navier Equations of Hydrodynamics 1. The State of the Fluid 2. The Equations of Motion 3. The Linearized Hydrodynamic Equations 4. Thermodynamic Discussion of the Compressibility 5. The Linearized Wave Equation for a Nonviscous Fluid 6. Viscosity 7. The Stokes-Navier Equation. "Classical" Sound Absorption 8. Formal Introduction of Volume Viscosity II. General Considerations on Relaxation 9. General Discussion of Resonance and Relaxation Phenomena 10. Energy Exchange between Internal and External Degrees of Freedom as Relaxation Phenomenon 11. The Effect of Slow Energy Exchange on Sound Propagation 12. Discussion of the Dispersion Equation 13. Different Ways of Evaluating the Dispersion Curve 14. The Absorption Curve 15. Continuation of the Discussion of Absorption 16. Continuation of the Discussion of Absorption and Dispersion: Kneser's Expression. Calculation of Ceff 17. Exact Calculation of Absorption and Dispersion 18. Dependence on τ. Summary of Characteristic Times 19. Exchange of Energy and Relaxation Equation 20. General Discussion of the Case in Which More Than One Relaxation Time Exists 21. The Excitation of Different Degrees of Freedom Which Behave like a Group of Parallel Reactions 22. Excitations of Different Degrees of Freedom Which Behave like Chemical Reactions in Series. Classical Theory 23. Excitation in Series, with Exchange with Translational Energy (Quantum Theory) 24. The Solution of the General Equations of Excitation in Series 25. Relation of Dispersion and Absorption if More Than One Relaxation Time Is Present. General Shape of the Curves 26. Mixtures 27. The Effect of Chemical Reactions 28. Discussion of Special Cases. Various Orders of the Reaction 29. Continuation of Discussion. Different Values of V and H' 30. Does the "Volume Viscosity" Provide Actual Stresses, Even if the Relaxation Phenomenon is the Slow Energy Exchange with Internal Degrees of Freedom or a Chemical Reaction? 31. Thermodynamic Theory of Relaxation III. Special Topics 32. Scattering 33. Absorption of High Intensity Sound Waves B. Gases IV. Application of the General Formulas to Gases 34. Application of Previous Equations to Ideal Gases 35. Correction for Nonideality of the Gas 36. Viscosity and Relaxation Time for Translational Energy 37. Assumption That Only Binary Collisions are Effective 38. Low Frequency Absorption. Ratio of Relaxation Absorption to Classical Absorption at Maximum 39. Gas Mixtures 40. Triple Collisions in Pure Gases and in Mixtures 41. Additional Absorption in Mixtures V. Experimental Methods to Determine Velocity and Absorption of Ultrasonic Waves in Gases 42. Methods for Low Frequencies 43. The Ultrasonic Interferometer 44. Miscellaneous Methods 45. Aerodynamical Methods 46. Direct Methods for Measuring Absorption and Relaxation Time VI. Experimental Results in Molecules Without Electronic Excitation 47. Translational Relaxation in Monatomic Gases 48. Methods to Determine Rotational Relaxation Time 49. Results for Rotational Relaxation 50. Oxygen, Nitrogen, Air 51. Other Diatomic Molecules 52. Linear Triatomic Molecules 53. Nonlinear Triatomic Molecules and Four Atomic Molecules 54. Large Molecules VII. Theory of Vibrational and Rotational Energy Exchange 65. Introductory Remarks 56. The Theory of Landau and Teller (Classical) 67. Fundamental Quantum Consideration 58. Inelastic Scattering for an Exponential Interaction Potential 59. Introduction of a Better Interaction Potential 60. Tridimensional Case 61. Discussion of Scattering 62. Conclusion of the Tridimensional Calculation 63. Some Numerical Data. Effect of Molecular Frequency on Low Frequency Absorption 64. Simultaneous' Transitions in Rotational, Vibrational, and Translational Energy 65. Polyatomic Molecules. More Than One Vibrations Is Involved. Complex Collisions 66. Numerical Results for Diatomic and Linear Triatomic Molecules 67. Further Numerical Discussion of the Effect of Impurities, of Complex Collisions, and of Exact Resonance 68. Polyatomic Molecules: Methane and Chlorinated Methanes 69. Theory of Exchange of Rotational and Translational Energy 70. Energy Transfer and the Kinetics of Chemical Gas Reactions 71. Summary and Comparison of Theory and Experiment C Liquids VIII. General Review of Ultrasonic Absorption and Dispersion in Liquids 72. Classical Absorption 73. Absorption of Ultrasonic Waves in Liquids : The Situation in 1948. Pinkerton's Classification of Liquids 74. Developments Since 1948. Critical Review of Pinkerton's Classification 75. Velocity of Sound Waves of Ultrahigh Frequency (UHF) IX. Experimental Methods to Determine Dispersion and Absorption of Ultrasonic Waves in Liquids 76. Methods for Low Frequencies 77. The Ultrasonic Interferometer 78. Pulse Methods 79. Mechanical Method: Radiation Pressure Measurements 80. Optical Methods X. Review of Theories of Liquids 81. Introduction 82. Connection with Internal Pressure. Theory of Jäger 83. Heat Produced by Friction. Number of Collisions 84. Cubic Cell Model. Available Volume 85. Spherical Cell Model. "Free Volume" According to Thermodynamics 86. Spherical Cell Model. The Motion Treated as Simple Harmonic Motion 87. The Distribution Function; Calculation of η and η' 88. The Relaxation Time of the Distribution. Green's Theory 89. Brillouin's Theory of Viscosity 90. Eyring's Theory of Viscosity 91. The Theory of Bulk Viscosity by Gierer and Wirtz 92. Theory of Relaxation Time. Theory of Absolute Reaction Rates XI. Kneser Liquids 93. Discussion of Specific Heats in Nonassociated Organic Liquids with Molecules of Moderate Size 94. A Cooperative Theory of Relaxation Time for Kneser Liquids 95. Comparison of Relaxation Time in the Gaseous and Liquid States. Thermal Relaxation as due to Interaction between a Pair of Molecules 96. Temperature Dependence of the Absorption in Kneser Liquids 97. Carbon Disulfide CS2 98. Relaxation due to Rotational Isomerism 99. Liquid Mixtures XII. Associated Liquids and Liquids with High Viscosity 100. The Theory of Hall 101. Eucken's Theory of the Constitution of Water 102. The Effect of Pressure on Sound Absorption in Water 103. The Associated Liquids (Other than Water) and the Glassy State 104. Elastic Moduli of Liquids 105. Distribution of Relaxation Times 106. Absorption and Dispersion Measurements in Glycerol 107. Absorption and Dispersion in η-Propyl Alcohol 108. Transversal or Shear Waves in Liquids 109. Compressional Relaxation in Associated Liquids. Comparison with Shear Relaxation 110. Velocity Dispersion in Associated Liquids 111. Numerical Relationships Between the Moduli 112. The Temperature Dependence of Elastic Moduli of Liquids 113. The Origin of Volume Viscosity in Associated Liquids 114. The Relation of Ultrasonic and Dielectric Relaxation Times 115. Ultrasonic Hysteresis at High Frequencies 116. Dissociation of Dimers: Acetic and Propionic Acids 117. Mixtures Containing Associated Liquids 118. Effect of Pressure on Ultrasonic Relaxation in Liquids Author Index Subject Index